Is (1+tan^2(x))sin^2(x)=tan^2(x) ?

The answer to whether (1+tan^2(x))sin^2(x)=tan^2(x) is True

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prove (1+tan^2(x))sin^2(x)=tan^2(x)

prove

(1 + tan^{2} (x)) sin^{2} (x) = tan^{2} (x)

True

Solution steps

(1 + tan^{2} (x)) sin^{2} (x) = tan^{2} (x)

Manipulating left side

(1 + tan^{2} (x)) sin^{2} (x)

Rewrite using trig identities

= sec^{2} (x) sin^{2} (x)

Express with sin, cos

= \frac{sin ^{2} ( x )}{cos ^{2} ( x )}

Rewrite using trig identities

tan^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

sec^{2} (x) = (sec (x))^{2}

cos^{3} (θ) + cos (θ) sin^{2} (θ) = cos (θ)

csc (θ) sin (θ) = 1

(1 - cos (x))^{2} = csc^{2} (x) - 2 cot (x)

cos^{2} (9 x) - sin^{2} (9 x) = cos (18 x)

Is (1+tan^2(x))sin^2(x)=tan^2(x) ?
The answer to whether (1+tan^2(x))sin^2(x)=tan^2(x) is True